How can I solve this problem
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How can I solve this problem

[From: ] [author: ] [Date: 12-06-19] [Hit: ]
The vertex represents the maximum.The max occurs when there are 5 extra people, which is 25 people, who would pay 30-5= 25 dollars each.Hoping this helps!Let p = # of people above 20 and f(p) = price for p people beyond 20.......
"A restaurant owner said that the total of a meal is 600$ for 20 people. For every additonal client in the group, there will be a 1$ deduction for the individual price". What is the maximum profit that this owner can get?

I'm having problems with this. Keep in mind that this is tenth grade quadratic systems...

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Total meal for 20 people is 20*30= 600
Let x be additional people over 20
So total people= 20+x
Price = 30-x

Total of meal = (20+x)(30-x)= -x^2+10x +600

This is a parabola that opens down. The vertex represents the maximum.

X= -b/(2a)= -10/(-2)= 5

The max occurs when there are 5 extra people, which is 25 people, who would pay 30-5= 25 dollars each.

Cost = 25*25= 625 dollars

Hoping this helps!

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price per person at 20 people = 600/20 = $30
Let p = # of people above 20 and f(p) = price for p people beyond 20.
f(p) = (20 + p)(30 - p) = 600 + 10p - p^2
f(p) has a maximum where f '(p) = 0 and f ''(p) < 0.
f '(p) = 10 - 2p
0 = 10 - 2p
p = 5
f ''(p) = -2 < 0 for all p so we know the maximum occus at p = 5.
Maximum profit = f(5) = 25(25) = $625
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